{"id":279566,"date":"2025-08-04T08:01:02","date_gmt":"2025-08-04T08:01:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=279566"},"modified":"2025-08-04T08:01:05","modified_gmt":"2025-08-04T08:01:05","slug":"fraction-285%e2%96%a1-of-a-semicircle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/fraction-285%e2%96%a1-of-a-semicircle\/","title":{"rendered":"Fraction: 285\u00b0=\u25a1 of a semicircle"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Here are the solutions to the problems presented in the image.<\/p>\n\n\n\n

Fraction:<\/strong> 285\u00b0 = 19\/12<\/strong> of a semicircle
Angle measure:<\/strong> 285\u00b0 = 19\u03c0\/12<\/strong> radians<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

1. Finding the Fraction of a Semicircle<\/strong><\/p>\n\n\n\n

To express 285 degrees as a fraction of a semicircle, you first need to know how many degrees are in a semicircle. A full circle contains 360 degrees, so a semicircle, being half of a circle, contains 360 \/ 2 = 180 degrees.<\/p>\n\n\n\n

Next, you create a fraction by placing the given angle (285\u00b0) over the angle of a semicircle (180\u00b0):<\/p>\n\n\n\n

Fraction = 285 \/ 180<\/p>\n\n\n\n

To simplify this fraction, you find the greatest common divisor (GCD) for both the numerator and the denominator. Both numbers are divisible by 5:
285 \u00f7 5 = 57
180 \u00f7 5 = 36
This gives the fraction 57\/36.<\/p>\n\n\n\n

Now, we can simplify this fraction further. Both 57 and 36 are divisible by 3:
57 \u00f7 3 = 19
36 \u00f7 3 = 12
This simplifies the fraction to 19\/12. Since 19 is a prime number, the fraction is in its simplest form. Thus, 285\u00b0 is 19\/12 of a semicircle.<\/p>\n\n\n\n

2. Converting Degrees to Radians<\/strong><\/p>\n\n\n\n

To convert an angle from degrees to radians, you multiply the degree measure by the conversion factor \u03c0\/180\u00b0.<\/p>\n\n\n\n

The formula is: Radians = Degrees \u00d7 (\u03c0 \/ 180\u00b0)<\/p>\n\n\n\n

Applying this to 285 degrees:
Radians = 285 \u00d7 (\u03c0 \/ 180)
Radians = (285\u03c0) \/ 180<\/p>\n\n\n\n

As we did in the first problem, we simplify the fraction 285\/180. We already determined that this simplifies to 19\/12.<\/p>\n\n\n\n

Therefore, the angle measure of 285\u00b0 in radians is 19\u03c0\/12.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The Correct Answer and Explanation is: Here are the solutions to the problems presented in the image. Fraction: 285\u00b0 = 19\/12 of a semicircleAngle measure: 285\u00b0 = 19\u03c0\/12 radians Explanation 1. Finding the Fraction of a Semicircle To express 285 degrees as a fraction of a semicircle, you first need to know how many degrees are in a semicircle. A full […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-279566","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=279566"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/279566\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=279566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=279566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=279566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}